Difficulty estimation of number place puzzle and its problem generation support

This paper proposes a method for estimating difficulty of number place puzzle problem. The proposed method formulates a number place problem as a graph colorability (COL) problem, solves it by a general COL solver, and ranks its difficulty from the search cost the solver spends until a solution is found. Compared to previous work, the method is quite fast and plural trials are not necessary due to no stochastic process in it. This paper also proposes a tool for supporting number place problem design. The tool uses the proposed difficulty estimation method, and is implemented on mobile phone platform “Google Android.” Experiments have shown that the proposed method could roughly estimate difficulty of number place problem instances.